A spinner contains four sections: red, blue, green, and yellow. Joaquin spins the spinner twice. The set of outcomes is given as cap s is equal to RB, RG, RY, RR, BR, BG, BY, BB, GR, GB, GY, GG, YR, YB, YG, YY If the random variable is “yellow cap y ,” which of the following is the correct probability distribution?
Answer
A
Table with 2 columns and 4 rows.Row 1: Column 1, 'Yellow: cap x'; Column 2, 'Probability: cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 5' Row 3: Column 1, '1'; Column 2, '0 point 2 5' Row 4: Column 1, '2'; Column 2, '0 point 2 5'
B
Table with 2 columns and 4 rows.Row 1: Column 1, 'Yellow: cap x'; Column 2, 'Probability: cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 7 5' Row 3: Column 1, '1'; Column 2, '0 point 2 5' Row 4: Column 1, '2'; Column 2, '0'
C
Table with 2 columns and 4 rows.Row 1: Column 1, 'Yellow: cap x'; Column 2, 'Probability: cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 5' Row 3: Column 1, '1'; Column 2, '0 point 3 7 5' Row 4: Column 1, '2'; Column 2, '0 point 1 2 5'
D
Table with 2 columns and 4 rows.Row 1: Column 1, 'Yellow: cap x'; Column 2, 'Probability: cap p sub cap x times x' Row 2: Column 1, '0'; Column 2, '0 point 5 6 2 5' Row 3: Column 1, '1'; Column 2, '0 point 3 7 5' Row 4: Column 1, '2'; Column 2, '0 point 0 6 2 5'
Explanation
Each spin has a 1/4 chance of landing on yellow and a 3/4 chance of not landing on yellow. In 16 equally likely outcomes, 9 have no yellow, 6 have exactly one yellow, and 1 has two yellows. Thus the probabilities are 9/16 = 0.5625, 6/16 = 0.375, and 1/16 = 0.0625, respectively, matching the table with 0, 1, and 2 yellows in choice A.
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