Pick three cards randomly from a usual deck with 52 cards. What is the probabili
ID: 3204457 • Letter: P
Question
Pick three cards randomly from a usual deck with 52 cards. What is the probability that you can have a pair (like 232, 344, 555) Pick two cards randomly from a usual deck with 52 cards. Let X be the number of Ace card(s) you can get. Find the distribution of X. Suppose in a class, there are 10 boys and 8 girls. Pick two kids randomly, and let X be the number of girls. Write the distribution of X. The number of pizzas delivered to university students each month is a random variable with the following distribution. X 0 1 2 3 P(X) .1 .3 .4 .2 Calculate the mean number of pizzas delivered to each student. If the pizzeria makes a profit of S3 per pizza, determine the mean of the profits made from per student.Explanation / Answer
As multiple questions are posted, only the first one will be answered.
1. Number of ways in which a pair will appear in a selection of 3 cards = 52C1 * 3C1 * 50C1
[First we select one card from 52, and the next card should be out of the remaining 3 shapes of the first card, to form a pair, and the 3rd card can be any from the remaining 50 cards]
Total number of ways of selecting 3 cards from 52 = 52C3
Required probability = 52C1 * 3C1 * 50C1 / 52C3 = 0.3529