The two dice are independent, i.e. the result of one die does not infuence the result of the other. In this case, the probability of a complex event is the product of the probabilities of the simple events. For every die, there are #3# odd outcomes and #3# even outcomes. So, the probability of getting an odd number is #3/6=1/2# So, the probability that this happens with both dice is #1/2*1/2=1/4# In this case, it is actually easy to enumerate the "good" outcomes: there are #36# outcomes in total (all numbers from #1# to #6# for one die and the same for the other die). The good outcomes are #(1,1)#, #(1,3)#, #(1,5)# #(3,1)#, #(3,3)#, #(3,5)# #(5,1)#, #(5,3)#, #(5,5)# And in fact, #9# good outcomes over #36# total outcomes means #9/36 = 1/4# Probability is a measure of the possibility of how likely an event will occur. It is a value between 0 and 1 which shows us how favorable is the occurrence of a condition. If the probability of an event is nearer to 0, let’s say 0.2 or 0.13 then the possibility of its occurrence is less. Whereas if the probability of an event is nearer to 1, lets say 0.92 or 0.88 then it is much favourable to occur. Probability of an event The probability of an event can be defined as a number of favorable outcomes upon the total number of outcomes.
Some terms related to probability
When two dice are rolled what is the probability of getting same number on both?
Sample QuestionsQuestion 1: Find the probability of getting odd number on first dice and even number on other dice when two dice are thrown simultaneously. Answer:
Question 2: If two dice are thrown together then find the probability of getting 1 or 2 on either of the dice. Answer:
Question 3: In an event 2 dice are thrown simultaneously. Find the probability of getting prime number on first dice. Answer:
Question 4: Three coins are tossed together find the probability of getting at least one head and one tail. Answer:
Question 5: Find the probability of getting at least two tails when a coin is tossed three times. Answer:
Probability of occurrence of an event (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),Outcomes are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6) , (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) , (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) Total no.of outcomes are 36 In that only (1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1) are our desired outputs as there sum is less than 6 Therefore no.of desired outcomes are 10 Therefore, the probability of getting a sum less than 6 Conclusion: Probability of getting a sum less than 6, when two dice are rolled is 5/18 Probability of occurrence of an event Total doublets are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)In (a, b) if a=b then it is called a doublet In (a, b) if a=b and if a, b both are odd then it is called a doublet Odd doublets are (1, 1), (3, 3), (5, 5) Outcomes are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6) , (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) , (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) Conclusion: Probability of getting doublet of odd numbers, when two dice are rolled is 1/12 Probability of occurrence of an event (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),Outcomes are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6) , (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6) , (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6) Total no.of outcomes are 36 Desired outputs are (1, 1), (1, 2), (1, 4), (1, 6), (2, 1), (2, 3), (2, 5), (3, 2), (3, 4), (4, 1), (4, 3), (5, 2), (5, 6), (6, 1), (6, 5) Total no.of desired outputs are 15 Therefore, probability of getting the sum as a prime number Conclusion: Probability of getting the sum as a prime number, when two dice are rolled is 5/12 |