To find the probability distribution for the number of jellies Jemeel chooses, we calculate the probability for each possible number of jellies (0, 1, 2, 3) out of 3 sweets chosen.

There are a total of 8 sweets (5 jellies and 3 chocolates), and Jemeel chooses 3 sweets. The total number of ways to choose 3 sweets from 8 is \(\binom{8}{3} = 56\).

Probability of choosing 0 jellies:

Choose 3 chocolates from 3: \(\binom{3}{3} = 1\)

Probability: \(\frac{1}{56}\)

Probability of choosing 1 jelly:

Choose 1 jelly from 5 and 2 chocolates from 3: \(\binom{5}{1} \times \binom{3}{2} = 5 \times 3 = 15\)

Probability: \(\frac{15}{56}\)

Probability of choosing 2 jellies:

Choose 2 jellies from 5 and 1 chocolate from 3: \(\binom{5}{2} \times \binom{3}{1} = 10 \times 3 = 30\)

Probability: \(\frac{30}{56}\)

Probability of choosing 3 jellies:

Choose 3 jellies from 5: \(\binom{5}{3} = 10\)

Probability: \(\frac{10}{56}\)

The probability distribution table is: