Question

a special deck of cards has ten cards. four are green (g), two are blue (b), and four are red (r). when a card is picked, the color of it is recorded. an experiment consists of first picking a card and then tossing a coin, which lands on heads (h) or tails (t).
part (a)
part (b)
let a be the event that a blue card is picked first, followed by landing a head on the coin toss. find ( p(a) ) (enter your probability as a fraction.)
( p(a) = )
part (c)
part (d)

Explanation:

Step1: Find probability of picking a blue card

There are 2 blue cards out of 10 total cards. So the probability of picking a blue card, \( P(\text{blue}) = \frac{2}{10} \).

Step2: Find probability of coin landing on heads

A coin has 2 sides, so the probability of landing on heads, \( P(\text{heads}) = \frac{1}{2} \).

Step3: Find probability of both events (since they are independent)

For independent events, \( P(A) = P(\text{blue}) \times P(\text{heads}) \). Substituting the values, we get \( P(A) = \frac{2}{10} \times \frac{1}{2} \). Simplifying this, \( \frac{2 \times 1}{10 \times 2} = \frac{2}{20} = \frac{1}{10} \).

Answer:

\(\frac{1}{10}\)