Explanation:
since both spins are independent events (one does not have any impact on the other), the sequence does not matter. the probability of first blue and then gray is the same as first gray and then blue.
it is the probability of getting 1 gray and 1 blue result.
a probability is always the ratio
desired cases / totally possible cases.
since 6/10 of the area of the spine are gray, and 4/10 of the area are blue, the probability for any single spin to result in gray is 6/10 = 3/5 = 0.6.
and the probability to result in blue is 4/10 = 2/5 = 0.4
the probability to get 1 gray and 1 blue is then the product of both probabilities :
0.6 × 0.4 = 0.24
it is like rolling a die twice and asking for e.g. two 6s or any other combination of 2 specific numbers. that probability is
1/6 × 1/6 = 1/36
FYI :
the probability of getting gray twice is then
0.6 × 0.6 = 0.36
the probability of getting blue twice is
0.4 × 0.4 = 0.16
as mentioned to get gray first and blue second is
0.6 × 0.4 = 0.24
to get blue first and gray second
0.4 × 0.6 = 0.24
and these are all the possible results you can get in 2 spins.
therefore, the probability for any of them is
0.36 + 0.16 + 0.24 + 0.24 = 1