Question

According to a theory in​ genetics, if tall and colorful plants are crossed with short and colorless​ plants, four types of plants will​ result: tall and​ colorful, tall and​ colorless, short and​ colorful, and short and​ colorless, with corresponding probabilities: 0.37, 0.42, 0.11 and 0.10. ten plants are selected. find the probability that 5 will be tall and colorful, 2 will be tall and colorless, 2 will be short and colorful, and 1 will be short and colorless.

Answer 1

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Answer:

For 5 tall and colorful => Choosing 5 from 10 and multiplying by probability 0.37 = 10C5 * 0.37^5

For 2 tall and colorless => Choosing 2 from remaining 5 and multiplying by probability 0.42 = 5C2*0.42^2

For 2 short and colorful=> Choosing 2 from remaining 3 and multiplying by probability 0.11 = 3C2*0.11^2

For 1 short and colorless=> Choosing 1 from remaining 1 and multiplying by probability 0.10 = 1C1 *0.10

Hence total Probability = 10C5 * 0.37^5 * 5C2*0.42^2 * 3C2*0.11^2 *1C1 *0.10

= 0.0112