Two cards will be drawn from a standard deck without replacement. The even-numbe

Question

Two cards will be drawn from a standard deck without replacement. The even-numbered cards are the 2, 4, 6, 8, and 10 in each of the four suits.

(a) Are drawing an even-numbered card on the first draw and drawing an even-numbered card on the second draw mutually exclusive?

(b) Find the chance of drawing an even-numbered card at least once in the 2 draws (that is, on the 1st draw or on the 2nd draw or on both).

(c) Are drawing an even-numbered card on the first draw and drawing an even-numbered card on the second draw independent?

(d) Find the chance of drawing two even-numbered cards (drawing even-numbered cards on both draws).

Explanation / Answer

a) The events are not mutually exclusive because they both can happen at the same time (even number of forst and second draw is possible)

b) P(drawing an even numbered cars at least once) = 1 - P(not drawing an even number on two draws)

= 1 - (8x4/52)x(31/52)

= 0.633

c) When even number is not drawn on first draw, the probability of getting an even number on second draw = 5x4/52 = 5/13

When an even numbered card is drawn on first draw, the probability of getting an even number on second draw = (5x4 - 1)/52

= 19/52

When an even number is drawn on first draw, it affects the probability of drawing an even number on second draw, and hence they are not independent events

d) P(two even numbered cards) = 20/52 x 19/52 = 0.1405

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.