Problem

You are certain to get 2 kings when selecting 50 cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive. The probability is (Type an integer or a decimal.)

Solution

Step 1 :First, we need to calculate the total number of ways to select 50 cards from a deck of 52 cards. This is given by the combination formula \(C(n, r) = \frac{n!}{(n-r)!r!}\), where \(n\) is the total number of items, and \(r\) is the number of items to choose. In this case, \(n = 52\) and \(r = 50\). The total number of ways is 1326.

Step 2 :Next, we need to calculate the total number of ways to select 2 kings from 4 kings. This is also given by the combination formula. In this case, \(n = 4\) and \(r = 2\). The total number of ways is 6.

Step 3 :Then, we need to calculate the total number of ways to select the remaining 48 cards from the remaining 48 cards (52 total cards - 4 kings). This is also given by the combination formula. In this case, \(n = 48\) and \(r = 48\). The total number of ways is 1.

Step 4 :The probability of getting 2 kings when selecting 50 cards from a shuffled deck is given by the formula: \(P(E) = \frac{C(4, 2) * C(48, 48)}{C(52, 50)}\)

Step 5 :Substituting the calculated values into the formula, we get \(P(E) = \frac{6 * 1}{1326} = 0.004524886877828055\)

Step 6 :Final Answer: The probability of getting 2 kings when selecting 50 cards from a shuffled deck is \(\boxed{0.0045}\)

From Solvely APP
Source: https://solvelyapp.com/problems/7245/

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