4 pointsTwo bags (𝐵1𝑎𝑛𝑑𝐵2)(B 1 andB 2 ) containing candies are placed on a table. Bag 𝐵1B 1 contains 7 cinnamon candies and 4 ginger candies. Bag 𝐵2B 2 contains 3 cinnamon candies and 8 ginger candies. The boxes are arranged such that the probability of selecting bag 𝐵1B 1 is 1⁄3 and the probability of selecting bag 𝐵2B 2 is 2⁄3. Suman is blindfolded and asked to select a candy. She will win a colour TV if she selects a cinnamon candy. Based on the given information, answer the questions (9) and (10).What is the probability that Suman will win the TV?7/332/111/213/33
Question
4 pointsTwo bags (𝐵1𝑎𝑛𝑑𝐵2)(B 1 andB 2 ) containing candies are placed on a table. Bag 𝐵1B 1 contains 7 cinnamon candies and 4 ginger candies. Bag 𝐵2B 2 contains 3 cinnamon candies and 8 ginger candies. The boxes are arranged such that the probability of selecting bag 𝐵1B 1 is 1⁄3 and the probability of selecting bag 𝐵2B 2 is 2⁄3. Suman is blindfolded and asked to select a candy. She will win a colour TV if she selects a cinnamon candy. Based on the given information, answer the questions (9) and (10).What is the probability that Suman will win the TV?7/332/111/213/33
Solution
To find the probability that Suman will win the TV, we need to calculate the total probability of drawing a cinnamon candy from either bag.
First, let's calculate the probability of drawing a cinnamon candy from each bag:
Bag B1: There are 7 cinnamon candies out of a total of 11 candies (7 cinnamon + 4 ginger), so the probability is 7/11.
Bag B2: There are 3 cinnamon candies out of a total of 11 candies (3 cinnamon + 8 ginger), so the probability is 3/11.
Next, we need to take into account the probability of selecting each bag:
The probability of selecting bag B1 is 1/3, and the probability of selecting bag B2 is 2/3.
So, the total probability of drawing a cinnamon candy is:
(Probability of selecting B1) * (Probability of drawing a cinnamon candy from B1) + (Probability of selecting B2) * (Probability of drawing a cinnamon candy from B2)
= (1/3 * 7/11) + (2/3 * 3/11)
= 7/33 + 6/33
= 13/33
So, the probability that Suman will win the TV is 13/33.
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