HOME WORK EXERCISE by kavita Umesh Joshi

A biased coin with P(Heads)=0.7 is tossed 6 times. What is the probability of getting at least 4 heads?

kavitaumeshjoshi2015 — 2025-01-21 12:20:39 UTC

kavitaumeshjoshi2015 — 2025-01-21 12:21:12 UTC

kavitaumeshjoshi2015 — 2025-01-21 12:21:48 UTC

Solution:

kavitaumeshjoshi2015 — 2025-01-21 12:22:32 UTC

jialuo2 — 2025-01-22 16:20:20 UTC

p = 0.7

n = 6

random value = 3 (4,5,6)

X (x = 4) = (6,4) * (0.7)^4 * (1 - 0.7)^6-4

≈ 0.32

X (x = 5) = (6,5) * (0.7)^5 * (1 - 0.7)^6-5

≈ 0.30

X (x = 6) = (6,6) * (0.7)^6 * (1 - 0.7)^6-6

≈ 0.12

0.32 + 0.30 + 0.12 = 0.74

0.74 * 100 = 74%

jialuo2 — 2025-01-22 19:34:15 UTC

p = 1/4 or 0.25

n = 15

random value = 5

X (x = 5) = (15, 5) (0.25)^5 * (1 - 0.25)^15 - 5

≈ 0.17

0.17 * 100 = 17%

2025-01-23 11:34:38 UTC

n= 15

p= 0.25

x= 5

=17%