Question

Suppose that you have 9 cards. 5 are green and 4 are yellow. The 5 green cards are numbered 1, 2, 3, 4, and 5. The 4 yellow cards are numbered 1, 2, 3, and 4. The cards are well shuffled. Suppose that you randomly draw two cards, one at a time, and without replacement. • G1 = first card is green • G2 = second card is green a) Draw a tree diagram of the situation. (Enter your answers as fractions.) b) Enter the probability as a fraction. P(G1 AND G2) = c)Enter the probability as a fraction. P(at least one green) = d)Enter the probability as a fraction. P(G2 | G1) = _______.

Answer 1

The probability of picking greens on both occasions will be 5/18.

How to explain the probability?

The probability of picking greens cards will be:

= 5/9 × 4/8

= 5/18

The probability of picking at least one green will be:

= 1 - P(both aren't green)

= 1 - (4/9 × 3/8)

= 1 - 1/6.

= 5/6

From the tree diagram, the probability as a fraction of P(G2 | G1) will be:

= 4/8 = 1/2

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