Shreyas went to the fair and played a game with three spinners. He spins each spinner once and wins a prize if he gets 2 blues and 1 red.

Using the principle of probability, the likelihood that Shreya wins by getting 2 blues and 1 red is 0.416

Creating an area model for the first two spinners :

___ G _ B _ B _ R _R _R

R_RG_RB_RB_RR_RR_RR

R_RG_RB_RB_RR_RR_RR

B_BG_BB_BB_BR_BR_BR

B_BG_BB_BB_BR_BR_BR

B_BG_BB_BB_BR_BR_BR

B_BG_BB_BB_BR_BR_BR

G_GG_GB_GB_GR_GR_GR

G_GG_GB_GB_GR_GR_GR

Creating an area model or tree diagram for the third spinner would result in a sample space of (48 × 12) = 576 combinations.

However, the probability that Shreya would win can be obtained thus :

To win he needs to pick get 2 blues and 1 red in any order :

3! = 3 × 2 × 1 = 6 ways

P(BBR) = 1/3 × 4/8 × 5/12 = 0.0694444

P(winning) = 6 × 0.0694444 = 0.416

Therefore, the probability that Shreya wins is 0.416.

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_______________________________________________
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