The times taken by 135 runners to complete a cross-country course were recorded. The results are summarised in the table. Time (t minutes) 20<t≤30 30<t≤35 35<t≤40 40<t≤50 50<t≤70 Number of runners 15 30 40 35 15 A bag contains R red beads and B blue beads. Two beads are chosen, at random, without replacement. The tree diagram shows the possible outcomes and their probabilities. [Figure 10.1 - Tree diagram description: First bead: Red (prob 3/5), Blue (prob 2/5). Second bead (if First Red): Red (prob 11/19), Blue (prob 8/19). Second bead (if First Blue): Red (prob 12/19), Blue (prob 7/19).]

1. (a)(i)On the grid, draw a histogram to represent this information.[3]
2. (a)(ii)Calculate an estimate of the mean time.[3]
3. (b)(i)Calculate the probability that both beads are red.[1]
4. (b)(ii)Calculate the probability that the two beads are different colours.[2]
5. (b)(iii)What is the value of R?[1]
6. (b)(iv)Of the red beads, half have a yellow spot. Calculate the probability that, of the two chosen beads, neither has a yellow spot.[2]

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