No worries! We‘ve got your back. Try BYJU‘S free classes today! No worries! We‘ve got your back. Try BYJU‘S free classes today! Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses No worries! We‘ve got your back. Try BYJU‘S free classes today! Let X denote the number of aces in a sample of 2 cards drawn from a well-shuffled pack of 52 playing cards. Then, X can take the values 0, 1 and 2. \[P\left( X = 0 \right)\] \[ = P\left( \text{ no ace } \right)\] \[ = \frac{48}{52} \times \frac{48}{52}\] \[ = \frac{12 \times 12}{13 \times 13}\] \[ = \frac{144}{169}\] \[P\left( X = 1 \right)\] \[ = P\left( 1 \text{ ace } \right)\] \[ = \frac{4}{52} \times \frac{48}{52}\] \[ = \frac{2 \times 12}{13 \times 13}\] \[ = \frac{24}{169}\] \[P\left( X = 2 \right)\] \[ = P\left( 2 \text{ aces } \right)\] \[ = \frac{4}{52} \times \frac{4}{52}\] \[ = \frac{1 \times 1}{13 \times 13}\] \[ = \frac{1}{169}\] Thus, the probability distribution of X is given by
Page 2Let X denote the number of kings in a sample of 2 cards drawn from a well-shuffled pack of 52 playing cards. Then, X can take the values 0, 1 and 2. \[P\left( X = 0 \right)\] \[ = P\left( \text{ no kings } \right)\] \[ = \frac{48}{52} \times \frac{48}{52}\] \[ = \frac{12 \times 12}{13 \times 13}\] \[ = \frac{144}{169}\] \[P\left( X = 1 \right)\] \[ = P\left( 1 \text{ king } \right)\] \[ = \frac{4}{52} \times \frac{48}{52}\] \[ = \frac{2 \times 12}{13 \times 13}\] \[ = \frac{24}{169}\] \[P\left( X = 2 \right)\] \[ = P\left( 2 \text{ kings } \right)\] \[ = \frac{4}{52} \times \frac{4}{52}\] \[ = \frac{1 \times 1}{13 \times 13}\] \[ = \frac{1}{169}\] Thus, the probability distribution of X is given by
Page 3Let X denote the number of aces in a sample of 2 cards drawn from a well-shuffled pack of 52 playing cards. Then, X can take the values 0, 1 and 2. \[P\left( X = 0 \right)\] \[ = P\left( \text{ no ace } \right)\] \[ = \frac{48}{52} \times \frac{47}{51}\] \[ = \frac{2256}{2652}\] \[ = \frac{188}{221}\] \[P\left( X = 1 \right)\] \[ = P\left( 1 \text{ ace } \right)\] \[ = \frac{4}{52} \times \frac{48}{51} + \frac{48}{52} \times \frac{4}{51}\] \[ = \frac{384}{2652}\] \[ = \frac{32}{221}\] \[P\left( X = 2 \right)\] \[ = P\left( 2 \text{ aces } \right)\] \[ = \frac{4}{52} \times \frac{3}{51}\] \[ = \frac{12}{2652}\] \[ = \frac{1}{221}\] Thus, the probability distribution of X is given by
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