Calculating Binomial Probabilities (AQA A-Level Mathematics): Revision Notes

Example:

Calculator Steps:

1. Binomial CD
2. Enter values: $X = 10, N = 20, p = 0.3$
3. Result: $P = :highlight[0.9828551835]$

Example: The random variable $X \sim B(20, 0.35)$.

Questions:

Find: a) $P(X \leq 10)$ b) $P(X > 6)$ c) $P(X=5)$

d) $P(2 \leq X \leq 7)$

a) $P(X \leq 10) = :highlight[0.9468333856]$

b) $P(X > 6) = 1 - P(X \leq 6)$

• Do want $7, 8, 9, ...$
• Don't want $6, 5, 4, ...$
• $P(X > 6) = :highlight[0.5833745818]$

Key Point: If given any inequality that is not $\leq$, we must find a calculation with the same answer that does involve $\leq$.

c) $P(2 \leq X \leq 7)$

Calculator Steps:

4. Binomial PD
5. Enter values: $X = 5, N = 20, p = 0.35$
6. Result: $P = :highlight[0.1271991857]$

d) $\ P(2 \leq X \leq 7)$

Calculator Steps:

7. Binomial CD
8. List: Variable
9. Enter values: $N = 20, p = 0.35$
10. Result for $P(X \leq 7): :highlight[0.6010266036]$
11. Result for $P(X \leq 1): :highlight[2.1331 × 10^{-3}]$

To find $P(2 \leq X \leq 7)$: