Maths · Rung 18 of 30

Two events

Two independent events (two coins, two dice) multiply: P(heads and heads) = 1/2 × 1/2 = 1/4. Without replacement the second draw changes: fewer balls remain. 'At least one' is computed through its opposite: 1 − P(none).

Where this sits

This is where the ladder starts: nothing is needed before it.

Exercises from this rung

Generated by the app, from easiest to hardest

  1. You roll two dice. What is the probability they add up to 7?

    • 1/6
    • 6/11
    • 1/2
    • 7/36

    Why There are 36 equally likely outcomes. 6 of them add up to 7, so 6/36 = 1/6.

    easier

  2. You roll two dice. What is the probability they add up to 4?

    • 1/4
    • 1/6
    • 1/9
    • 1/12

    Why There are 36 equally likely outcomes. 3 of them add up to 4, so 3/36 = 1/12.

    in between

  3. You draw two balls in a row without putting them back. What is the probability both are blue?

    • 3/14
    • 1/4
    • 3/7
    • 1/2

    Why First blue: 4/8. Second blue, one fewer: 3/7. Product: 12/56 = 3/14.

    harder