Question

Rashid is playing a game where he selects a card from a deck of four cards, labeled 1, 2, 3, or 4. the possible cards and probabilities are shown in the chart below.

card probability
1 20%
2 32%
3 39%
4 9%
what is the expected value for the card that rashid selects?
A. 2.45
B. 2.41
C. 2.37
D. 2.5

Answer 1

The expected value of the card Rashid selects is 2.37. The correct answer is option C.

Step-by-step explanation:

Rashid is playing a game where he selects a card from a deck of four cards, labeled 1, 2, 3, or 4. The expected value for the card that Rashid selects is calculated by multiplying each card's value by its probability of being selected and then summing these products. Here is the step-by-step calculation:

• For card 1 (probability 20% or 0.20), the expected value is 1 × 0.20 = 0.20.
• For card 2 (probability 32% or 0.32), the expected value is 2 × 0.32 = 0.64.
• For card 3 (probability 39% or 0.39), the expected value is 3 × 0.39 = 1.17.
• For card 4 (probability 9% or 0.09), the expected value is 4 × 0.09 = 0.36.

Adding these values together gives us:

0.20 + 0.64 + 1.17 + 0.36 = 2.37

Therefore, the expected value for the card Rashid selects is 2.37, which corresponds to option C.