probability questions from Lumosity I don't understand

Question

q1 chance of (crown and then red) = 1/4 x chance of purple

a1 crown, crown, red, purple,purple

q2 chance of (red or green) = chance of 2 stars in a row

a2 heart, heart, heart, star, star

Need explanation on HOW to get these answers.

Thanks,

Linda

Answer 1

I can only answer the first question; the second question is lacking information about what is red and what is green.

For question 1, the probability of picking a crown initially is 2/5. After you have picked that crown, now the probability of picking a red is 1/4. So the probability of picking both is 2/5 * 1/4 = 2/20.

The probability (in a completely separate event) of picking a star is 2/5 and 1/4 * 2/5 = 2/20.

So the two events have the same probability