Probability that less than 4 of the covers streamed were by male singers

To calculate the probability that less than 4 of the covers streamed were by male singers, we can use the concept of binomial probability.

Let’s denote:

– n = total number of covers streamed (30)
– k = number of covers by male singers (0, 1, 2, or 3)
– p = probability of a cover being by a male singer (12/60 = 0.2)
– q = probability of a cover NOT being by a male singer (1 – p = 0.8)

The probability of exactly k successes (covers by male singers) out of n trials is given by the binomial probability formula:
[ P(X = k) = \binom{n}{k} \times p^k \times q^{n-k} ]

Now, we need to calculate the probabilities for k = 0, 1, 2, and 3 covers by male singers and sum them up to find the total probability of less than 4 covers being by male singers:
[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) ]

Let’s calculate these probabilities:

– For k = 0: [ P(X = 0) = \binom{30}{0} \times 0.2^0 \times 0.8^{30} ]
– For k = 1: [ P(X = 1) = \binom{30}{1} \times 0.2^1 \times 0.8^{29} ]
– For k = 2: [ P(X = 2) = \binom{30}{2} \times 0.2^2 \times 0.8^{28} ]
– For k = 3: [ P(X = 3) = \binom{30}{3} \times 0.2^3 \times 0.8^{27} ]

After calculating these probabilities and summing them up, we will get the total probability of less than 4 covers being by male singers.

Let me perform these calculations for you. Stay tuned for the results.